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# Degree of convergence of a function in generalized Zygmund space

• *Corresponding author: M. Mursaleen
• In this paper, we obtain the results on the degree of convergence of a function of Fourier series in generalized Zygmund space using deferred Cesàro-generalized Nörlund $(D^{h}_{g}N^{a,b})$ transformation. Important corollaries are deduced from our main results. Some applications are also given in support of our main results.

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

 Citation:

• Figure 1.  Degree of convergence of function $f$

Figure 2.  Degree of convergence of function $f$

Table 1.  Degree of convergence of $f$ for different $n$

 $n$ Degree of convergence of $f$ 100 1.2575829 1000 1.1507909 10000 1.1082121 50000 1.0911295 100000 1.0854078 500000 1.0746045 1000000 1.0707630 . . . . $\infty$ 1

Table 2.  Degree of convergence of $f$ for different $n$

 $n$ Degree of convergence of $f$ 100 3.8368 1000 3.5991 10000 3.4794 50000 3.4274 100000 3.4096 500000 3.3759 1000000 3.3639 10000000 3.3315 100000000 3.3073 . . . . $\infty$ 3.1416
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Tables(2)